The Pseudo Projection Operator: Applications of Deep Learning to Projection Based Filtering in Non-Trivial Frequency Regimes

TL;DR

This paper introduces the Pseudo Projection Operator, a hybrid neural network model that improves frequency-based filtering by learning to select frequencies, outperforming traditional methods and autoencoders in noisy music datasets.

Contribution

The paper presents the PPO, a novel hybrid model combining projection operators with neural networks for adaptive frequency filtering in noisy signals.

Findings

PPO outperforms PO and DAE in most filtering experiments.

PPO effectively adapts to various noise types.

Potential applications in physical and biological sciences.

Abstract

Traditional frequency based projection filters, or projection operators (PO), separate signal and noise through a series of transformations which remove frequencies where noise is present. However, this technique relies on a priori knowledge of what frequencies contain signal and noise and that these frequencies do not overlap, which is difficult to achieve in practice. To address these issues, we introduce a PO-neural network hybrid model, the Pseudo Projection Operator (PPO), which leverages a neural network to perform frequency selection. We compare the filtering capabilities of a PPO, PO, and denoising autoencoder (DAE) on the University of Rochester Multi-Modal Music Performance Dataset with a variety of added noise types. In the majority of experiments, the PPO outperforms both the PO and DAE. Based upon these results, we suggest future application of the PPO to filtering problems in the physical and biological sciences.